Problem: The product of two positive integers is 18. The positive difference of these two integers is 3. What is the sum of the two integers?
Solution: 18 has 3 possible factorizations into pairs: $(1,18)$, $(2,9)$, and $(3,6)$. Only one of these, $(3,6)$, has difference 3, and it has sum $3+6=\boxed{9}$.